Math Physics:Fourier Analysis

Fourier Analysis of Periodic Signals

TODO

Sample Data for Fourier Analysis

Sample graphics file to Fourier transform

Download Sample time series data for 1D Fourier transform

Fourier Analysis of Non-periodic Signals

$f(x) = \int_{-\infty}^{\infty} \tilde{F}(k) e^{i k x} \, dk$

$\tilde{F}(k) = \frac{1}{2 \pi} \int_{-\infty}^{\infty} f(x) e^{-i k x} \, dx$

The Dirac Delta Function

$\delta(x - x') \equiv \frac{1}{2 \pi} \int_{-\infty}^{\infty} e^{i k (x - x')} \, dk$

$f(a) \equiv \int_{-\infty}^{\infty} f(x) \delta(x-a) \, dx$